Grobner bases for (partial) flag manifolds
JOURNAL OF SYMBOLIC COMPUTATION
Authors: Petrovic, Zoran Z.; Prvulovic, Branislav, I; Radovanovic, Marko
Abstract
For an arbitrary complex (partial) flag manifold F, a Grobner basis for the ideal which (in the Borel picture) determines the cohomology algebra H* (F; Z) is obtained. This Grobner basis is used to derive multiplication rules for a convenient additive basis of H* (F; Z) given in terms of Chern classes of the canonical bundles over F. The analogous Grobner bases related to the mod 2 cohomology of real flag manifolds are also presented. (C) 2019 Elsevier Ltd. All rights reserved.
Frequency and Type of Red Flags in Patients With Covid-19 and Headache: A Series of 104 Hospitalized Patients
HEADACHE
Authors: Garcia-Azorin, David; Trigo, Javier; Talavera, Blanca; Martinez-Pias, Enrique; Sierra, Alvaro; Porta-Etessam, Jesus; Arenillas, Juan F.; Guerrero, Angel L.
Abstract
Objective In this study, we aimed to evaluate the frequency of the main red flags in patients with headache who do have Covid-19. Background Headache is one of the most frequent neurologic symptoms of Coronavirus disease 2019 (Covid-19). Diagnosis of secondary headache disorders is still based on the presence of red flags. Design and Methods Cross-sectional study of hospitalized patients with confirmed Covid-19 disease. We interrogated every patient about the presence of headache and if so, a headache expert conducted a structured interview assessing the presence and type of the main red flags. We evaluated the presence of laboratory abnormalities on admission. Results We screened 576 consecutive patients, 130/576 (22.6%) described headache, and 104 were included in the study. Mean age of patients was 56.7 (standard deviation: 11.2) and 66/104 (63.4%) were female. Red flags concerning prior medical history were present in 79/104 (76.0%) cases, and those related to the headache itself were observed in 99/104 (95.2%) patients. All patients 104/104 (100%) described systemic symptoms and 86/104 (82.7%) some neurologic symptoms. Laboratory results were abnormal in 98/104 (94.2%) cases. The most frequent red flags were fever, in 93/104 (89.4%) patients, cough, in 89/104 (85.6% cases), and increased C-reactive protein in 84/100 (84.0%) cases. Conclusion In patients with Covid-19 that described the headache red flags were present in most cases. There was not any universal red flag, being necessary the comprehensive evaluation of all of them.